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The lengths of the sides of a triangle are \( 10 + x^2 \), \( 10 + x^2 \) and \( 20 - 2x^2 \). If for \( x = k \), the area of the triangle is maximum, then \( 3k^2 \) is equal to:

The angle of elevation of the top \( P \) of a vertical tower \( PQ \) of height \( 10 \) from a point \( A \) on the horizontal ground is \( 45^\circ \). Let \( R \) be a point on \( AQ \) and from a point \( B \), vertically above \( R \), the angle of elevation of \( P \) is \( 60^\circ \). If \( \angle BAQ = 30^\circ, AB = d \) and the area of the trapezium \( PQRB \) is \( \alpha \), then the ordered pair \( (d,\alpha) \) is:

Let \( a,b \) and \( c \) be the length of sides of a triangle \( ABC \) such that \( \dfrac{a+b}{7}=\dfrac{b+c}{8}=\dfrac{c+a}{9} \). If \( r \) and \( R \) the radius of incircle and radius of circumcircle of the triangle \( ABC \), respectively, then the value of \( \dfrac{R}{r} \) is equal to:

A tower \( PQ \) stands on a horizontal ground with base \( Q \) on the ground. The point \( R \) divides the tower in two parts such that \( QR = 15 \, \text{m} \). If from a point \( A \) on the ground the angle of elevation of \( R \) is \( 60^\circ \) and the part \( PR \) of the tower subtends an angle of \( 15^\circ \) at \( A \), then the height of the tower is :

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JEE Main 2022 25th July Morning Shift

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ